I'm curious as to how long the beer would take to oxidize or get off flavors while fermenting.

I did 1 week in primary and now its been in the secondary for another week (6.5 gal carboy). How long would I have to leave it in the secondary for it to oxidize? It's not something I want to do, I'm just curious because they recommend secondary being in a 5 gal carboy and I didn't have that on hand to minimize the oxygen contact.

Beer oxidizes pretty quickly, maybe a day or so of exposure to enough oxygen is plenty of time to cause noticeable damage. Small amounts of oxygen exposure might take a couple of months or more to show, however.

I think that putting 5 gallons of beer into a 6.5 gallon carboy probably falls into the second category, at worst. The CO2 that gets knocked out of the beer during the transfer will probably displace a lot of the oxygen in the headspace and the yeast is still active enough to scavenge a lot of the remaining oxygen.

You'll always be better off minimizing oxygen contact after fermentation. Using an appropriately sized secondary is one way to do that. Another thing to remember is that a secondary is usually completely optional, so you have the choice of skipping the secondary, leaving the beer in primary a little longer, and then going straight to kegs or bottles.